For instance John K. Davis, citing others, writes (pg 29)1 (citations and alternations are in Davis):

Many ethicists worry that a treatment for aging will cause a Malthusian disaster.2 Peter Singer, for example, asks us to “imagine that we develop and release [a] drug which will slow aging…. since people are living twice as long, there will soon be more people than the world can support” (Singer, 1991, pp. 138–139). Walter Glannon agrees: “[I]f everyone were to live much longer than they actually do, and the availability of resources did not increase, then more people competing for the same amount of resources over an extended period of time likely would lower the overall quality of life for all people” (Glannon, 2002b, p. 274).3 Leon Kass (2001, p. 19), and Daniel Kevles (1999) share this concern.

The final consideration is especially interesting. de Grey argues that whether to employ life extension treatments (in spite of overpopulation) is a choice to be made by future generations, and that by not making treatments available as soon as possible (by doing anti-aging research) we deny future generations this choice.

Overpopulation and animals

Davis says extending analysis to animals/other parts of the ecosystem is outside the scope of his paper, but this seems like a rather important thing to consider. To quote2 (pg 32):

Neither will I discuss the welfare of the nonhuman part of the ecosystem, whether of other species or of the ecosystem as a whole. Admittedly, a Malthusian crisis will affect every living thing on Earth eventually, and those harms and benefits are tremendously important for life-extension ethics. My argument will show that the total benefits of widely available life-extension almost certainly outweigh the total harms for humans, but I do not claim that this is true for the rest of the ecosystem.

Questions

Building off de Grey’s and Davis’ considerations, we can come up with a few questions regarding life extension and overpopulation:

To what extent will life extension lead to overpopulation?—Will it happen at all?

We can read de Grey from above. There is also Gavrioli and Gavrilova3; abstract:

A common objection against starting a large-scale biomedical war on aging is the fear of catastrophic population consequences (overpopulation). This fear is only exacerbated by the fact that no detailed demographic projections for radical life extension scenario have been conducted so far. This study explores different demographic scenarios and population projections, in order to clarify what could be the demographic consequences of a successful biomedical war on aging. A general conclusion of this study is that population changes are surprisingly slow in their response to a dramatic life extension. For example, we applied the cohort-component method of population projections to 2005 Swedish population for several scenarios of life extension and a fertility schedule observed in 2005. Even for very long 100-year projection horizon, with the most radical life extension scenario (assuming no aging at all after age 60), the total population increases by 22% only (from 9.1 to 11.0 million). Moreover, if some members of society reject to use new anti-aging technologies for some religious or any other reasons (inconvenience, non-compliance, fear of side effects, costs, etc.), then the total population size may even decrease over time. Thus, even in the case of the most radical life extension scenario, population growth could be relatively slow and may not necessarily lead to overpopulation. Therefore, the real concerns should be placed not on the threat of catastrophic population consequences (overpopulation), but rather on such potential obstacles to a success of biomedical war on aging, as scientific, organizational, and financial limitations.

What are some ways to deal with overpopulation if it does happen? (de Grey mentions denial of treatments and restriction of births, and briefly considers the possibility—or rather untenability—of expanding into space.) Indeed there is the keyhole solution of e.g. conditionally offering life extension treatment to people without children who have undergone vasectomy/tubal ligation.

Does not working on anti-aging research today deny the choice of future generations to employ life extension treatments?—If so, are we allowed to do this?

What are the likely consequences of overpopulation for humans? For animals? Is better or worse than having these people die instead?

Some of the objections to life-extension stem from a concern with overpopulation. I will show that whether or not the overpopulation threat is realistic, arguments from overpopulation cannot ethically demand halting the quest for, nor access to, life-extension. The reason for this is that we have a right to life, which entitles us not to have meaningful life denied to us against our will and which does not allow discrimination solely on the grounds of age. If the threat of overpopulation creates a rights conflict between the right to come into existence, the right to reproduce, the right to more opportunities and space (if, indeed, these rights can be successfully defended), and the right to life, the latter ought to be given precedence.

John K. Davis. “Life-extension and the Malthusian Objection”. Journal of Medicine and Philosophy, 30:27–44, 2005.